Electrical space resonator having a high ratio between quality factor and volume



Feb. 13, 1951 J. P. KINZER 2,541,925

- ELECTRICAL SPACE RESONATOR HAVING A HIGH RATIO BETWEEN QUALITY FACTOR AND VOLUME Filed April 15, 1945 4 Sheets-sheaf, 1

#vvavroa J. R K/NZER A T TOR/V5 Y Feb. 13, 1951 J. P. KINZER ELECTRICAL SPACE RESONATOR HAVING A HIGH RATIO BETWEEN QUALITY FACTOR AND VOLUME.

Filed April 13, 1945 4 Sheets-Sheet 2 .3 SE as N M/l/ENTOR J. P. K/NZER A T TORNE Y Feb. 13, 1951 J. P. KINZER 2,541,925

ELECTRICAL SPACE RESONATOR HAVING A HIGH RATIO BETWEEN'QUALITY FACTOR AND VOLUME Filed April 15, 1945 4-Sheets-Sheet 3 5 m Qj wk [L Q 5 t n w *5 g3 O a; I- N k: 5Q n =2 ll 51$? n Q23 i; SEQ I: SE

lNl/ENTOR JRK/NZER ATTORNEY Feb. 13, 1951 p, KINZER 2,541,925

ELECTRICAL SPACE RESONATOR HAVING A HIGH RATIO BETWEEN QUALITY FACTOR AND VOLUME Filed April 15, 1945 4 ShGtS-ShGGt 4 FIG. 5

l0 FIG. 7

J\I I T v T If 5 i 5 9375 FL -3c Q=2xl0 INVENTOR J. P. K/NZER BY z-MM- ATTORNEY Patented Feb. 13, 1951 ELECTRICAL SPACE RESONATOR HAVING A HIGH RATIO BETWEEN QUALITY FACTOR AND VOLUME John P. Kinzer, Ridgefield, N. .L, assignor to Bell Telephone Laboratories, Incorporated, New York, .N. Y., a corporation of New York Application April 13,1945, Serial No. 588,201

14 Claims.

This invention relates to electrical space resonators having a high ratio between quality factor and volume.

An object of the invention is to provide an electrical resonance chamber tunable over a range of frequencies for a desired mode of oscillation and so proportioned as to have a minimum of unwanted modes-of oscillation within that range.

Another object of the invention is to provide a high Q electrical resonance chamber having optimum dimensions from the standpoint of avoiding interfering modes of oscillation.

Another object of the invention to provide a cylindrical resonator having a minimum volume for a'given'Q.

Another object of the invention is to provide a cylindrical resonator having a maximum Q Where the frequency, the interior surface mate rial of the resonator and the volume .oithe resonator have each been prescribed.

A further object of the invention is to provide a tunable cylindrical resonator with coupling means which shall not interfere in any way with the tuning operaton and which shall be rela' tively free from the effects of that operation.

A quantity which is of "very great interest in connection with cavity resonators is the quality factor, Q, which may be'defined in terms of the ratio of the total energy stored up in the elecergy dissipated during each cycle.

energy stored energy lost per cycle (I) The ring time during which such aresonator will continue to oscillate after termination of the excitation is roughly proportional to Q.

If the material of which the cavity resonator is made were perfectly conducting the fields would be entirely confined to the space within the resonator there would be no losses and the Q would be infinite. Actually, however, the fields 'do penetrate the inner surface slightly giving rise to currents which result inenergy loss. The skin depth, 5, is therefore an important factor in dealing with Q. The skin depth is defined as that distance such that the current were uni formly distributed over that depth the losses would be the same as in the actual situation where the current falls off exponentially with distance below the surface. For non-magnetic materials the value of dis given by l p m 2ll' f where p is resistivity of the cavity 'wallin .ohmcm. and f is frequency measured incps.

In many applications and particularly in frequency ranges of the order of 10,000 megacycles (3 centimeters wavelength) the volume of reso nance chambers may be so great that largenumers of extraneous oscillations may occur. In practical applications of a resonant cavity the conditions of operation may require high magnitudes of Q. which can be attained only by the use of high order modes. The dimensions of the cavity then become large compared to the wavelength. The number of possible resonances and hence of possible extraneous or undesired oscillations is primarily a function of the volume of the cavity and increases with increasing dimensions. The difficulty of suppressing certain of these extraneous oscillations which may interfere with the desired operation makes it desirable to keep the cavity as small as possible consistent with meeting' the requirement of high Q so as to restrict the number of extraneous modes. This leads to the consideration of possible expedients for reducing the volume of the cavity resonator while [at the same time attaining the ,preassigned Q.

The volume of a'cavity resonator also is a very rough measure of its weight and of the space which must be provided for it. These factors add to the desirability of reducing the volume of the resonator as far as is consistent with obtaining the requisite electrical characteristics.

In the course or" a study directed toward reduction of the diameter of a resonance chamber so as to reduce the number of unwanted modes of oscillation .it transpired that with reduction of the diameter Q was also reduced but that the reduction in Q was much les than that expected. This led to the discovery that there is a minimum volume of resonance chamber capable of operating at a given Q and that this reduced volume is accompanied with relatively few extraneous modes of oscillation.

In accordance with the invention the dimensions of a minimum volume resonator are calculated by-the use of graphs prepared as presumed continuous functions of the relations between Q, A the free space wave length, 6 the skin depth of the material to be used at that particular wavelength, D the .internal diameter oi the cylindrical cavity, 'L the length of the cylindrical cavity and n the index of the mode denoting the number of half wavelength variations of field along the axis of the cylinder. From these graphs a magnitude of n is determined. Since it must be an integer the nearest integral value is chosen and the dameter and length of the-cylinder are then obtained by a very simple application of the graphs.

3 In the drawing Fig. 1 shows graphs of the relationship between and frequency for copper, aluminum and brass respectively over a wide frequency range;

Fig. 2 is a graph of the relation between 11., the index number of the mode of oscillation, and

Fig.4 shows schematically the structural proportions of a cylindrical cavity resonator providing a minimum volume for a definite preassigned Q in accordance with the invention;

Fig. 5 shows a sectional detail along the plane perpendicular to the longitudinal aXis through the line 55 of Fig. 4;

Fig. 6 is a bottom plan view of an alternative coupling to the resonator of Fig. 4, as viewed from within the resonator; and

Fig. 7 is a section alongthe line 'l----'! of Fig. 6 in the direction of the arrows.

By an involved mathematical process the details of which are unnecessary for an elucidation of this invention and are quite too involved to warrant their presentation in this specification it may be shown that for a cylindrical resonator operation in the TEOln mode permits the smallest volume for an assigned Q and free space wavelength Moreover, it may be shown, as disclosed in the Bell System Technical Journal, July 1947, pages 410 through 419 in an article by J. P. Kinzer and I. G. Wilson entitled Some Results on Cylindrical Cavity Resonators, that for such TEOln mode oscillations the optimum values of n, D and L are recoverable from the equations:

1.626 sin cos 1 (3) in which a is a solution of the transcendental equation (4) =L220 sec I (5) i=0.813 sec P (6) The use of the foregoing equations to provide suitable design graphs and the employment of the graphs for obtaining the actual dimensions of a cylindrical cavity resonator may be readily illustrated by the problem of designing a cavity resonator to have a preassigned Q=2 10 for a wavelength of 3 centimeters, that is, a frequency of approximately 10,000 megacycles. Assume that the material of the inner surface of the resonator is specified as copper.

From the graph of Fig. 1 which may be plotted from Equation 2 it may be observed that at the wavelength of 3 centimeters or a frequency of substantially 10x10 corresponding to the point P1 on the upper graph for copper,

v 4 Since Q=2 X 10 may be readily calculated to be 4.4.

We now turn to Fig. 2 which shows the relation of n to as derived from Equations 3 and 4. Although the graph of Fig. 2 presents a continuous function, the actual values of the index n in cavity resonators are, of course, restricted by physical considerations to integers. Hence a strictly accurate representation of the functional dependence of n on in the minimum V/Q cavity under discussion) would consist of a set of discrete points, one for each value of n. However, the continuous function plotted in Fig. 2 is such that its values for n integral coincides with the values of the true discontinuous function, that is, it passes through all the discrete points to which reference has been made.

Taking the value of 4A for turn to Fig. 2 to find the actual corresponding It turns out to be precisely 4.5. The diameter D and the length L may now be readily determined by reference to Fig. 3 in which L and Y have been plotted in terms of from Equations 5 and 6. From the upper graph we find that for or with i=3 centimeters, D=9.375 centimeters. From the lower graph, for the same magnitude of cg, %is-13.62

or L is 40.8 centimeters. To facilitate manufacture it may be expedient to choose a magnitude for D which while conforming to the principle of the invention may involve a slight comprise to permit use of standard commercial tubing in construction of the resonator.

The schematic structure of the resulting cavity resonator is shown in Fig. 4 in which the cylin- I ity resonator may be provided with an input coupling loop [2 introduced through anarrow slot aperture I3 in the Wall of the resonator at a point remote from the tuner i I. mote from the coupling loop I2, a second output At another point, re-

coupling loop M may be provided. Loops I2 and M extend in a plane transverse to the longitudinal axis of the resonator as will be apparent from Fig. which shows a detail of the structure including input loop E2. The plane of the loops l2 and i4 may be removed from the inner surface of the lower end of the resonator by a distance d which measures the separation of the planes of maximum intensity TED field from the end surface as determined by the equation In this equation k is an odd integer and with L=40 centimeters and 11:25 as in Fig. 4, (1 may have the values 0.8 centimeter, 2.4 centimeters or 4 centimeters, etc. It is preferable to place these loops at one of the maxim-um intensity field planes most remote from the tuner disc I! since this renders the loops relatively unaffected by variations in the position of that disc. In an alternative structure shown in Figs. 6 and 7, the .input and output loops l5 and I6 respectively are introduced through narrow slots i! and it in the lower end of the resonator. These apertures :each extend in a tangential direction and are located at a point substantially midway between the center and the periphery of the end, at which point the intensity of the electric vector is a max :imurn. Theoretically, for best results these apertures should be located at positions such that :their centers are at a distance of 024D from the central axis of the resonator at which maximum coupling to 'IEoin modes may be had. The re- :sulting structure serves to give the required Q at the preassigned frequency and for the interior surface prescribed. Moreover, it does this with :a minimum of volume which, in general, means a corresponding saving in material, in the masses which must be lifted or moved, in the space required and in the cost of the apparatus. Moreover, there is attained an additional advantage other than these which, in most cases, is still more important, that is, with the r duction in volume a very great reduction in the number of addi- 'tional resonances is effected, making it possible in many cases to avoid unwanted resonances which cause serious interference with the results desired.

It will be apparent that the invention is capable of utilization to take advantage of various design factors from which a choice is possible. The choice may lie between certain materials from which the resonator is constructed or with which its interior surface is coated to achieve a desirable skin depth or in utilization of the minimum Q which may be satisfactory for a given set of circumstances.

What is claimed is:

' l. A cylindrical resonator comprising a hollow shell of electrically conducting material designed to have a preassigned quality factor Q at a given 6 frequency f for oscillations of TEom mode, the material presenting a skin depth 5 at itsinner surface and the magnitudes of the length L and diameter D of the cylinder being substantially in accordance with L=)\(0.8l3 560 (1)) D= \(1.220 see (p) where A is the free space wavelength at frequency f and p is a solution of the transcendental equation 5 cos p3 cos (p=l 220 6Q whereby for a specified f and Q, the volume of the resonator is a minimum.

2. A cylindrical resonator in accordance with I claim 1 characterized in this, that one end of the hollow shell is closed by a movable tuning piston which is displaceable longitudinally of the chamber from a minimum frequency position at which l .626 sin (19 cos go to the nearest integral value with A signifying the free space length at frequency f and u being a solution of the transcendental equation 4. The structure of claim 3, wherein said resonator is provided with a tuning piston at one end and a flat plate at the opposite end, coupling loops inserted in said resonator in a plane of maximum field intensity for 'IEo modes and at a distance from the end plate of said resonator, where k is an odd integer, L is the length of the cylinder and n lc.

JOHN P. KINZER.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS Number Name Date 2,241,119 Dallenbach May 6, 1941 2,245,627 Varian June 17, 1941 2,281,550 Barrow May 5, 1942 2,356,414 Linder Aug. 22, 1944 2,362,209 Litton Nov. 7, 1944 2,439,388

Hansen Apr. 13, 1948 

